Impulse Control of Interest Rates

Most academic studies on interest rate dynamics and derivative pricing assume that interest rates move freely in an open market, while there has been relatively little attention paid to the situation where a nation's central bank has the power to intervene in the interest rate market. This paper examines the effect that a central bank's interventions have on longer term interest rate securities. We model the central bank's intervention as an impulse control problem on a very general class of stochastic processes. As there is no known solution methodology to solve the posed problem, we develop a computational method and provide all the necessary theoretical guarantees. Using this method we solve for the central bank's optimal control policy and also study the effect of this on longer term interest rate securities using a change of measure. The method developed here can easily be applied to a very wide range of impulse control problems beyond the realm of interest rate models